The D(2,1;\alpha) Particle

TL;DR

This paper explores the superalgebra D(2,1;α) as an extended BRST quantisation framework in 2D, proposing a scalar relativistic particle model with a superfield realization and cohomological analysis.

Contribution

It introduces an alternative interpretation of D(2,1;α) as a superalgebra in BRST quantisation and provides a superfield realization with physical state analysis.

Findings

Superfield realization of D(2,1;α) in 2D BRST framework

Identification of physical states via BRST cohomology

Conjecture of scalar relativistic particle model underlying the algebra

Abstract

The exceptional superalgebra $D(2,1;\alpha)$ has been classified as a candidate conformal supersymmetry algebra in two dimensions. We propose an alternative interpretation of it as extended BFV-BRST quantisation superalgebras in 2D ($D(2,1;1) \simeq osp(2,2|2)$). A superfield realization is presented wherein the standard extended phase space coordinates can be identified. The physical states are studied via the cohomology of the BRST operator. It is conjectured that the underlying model giving rise to this `quantisation' is that of a scalar relativistic particle in 1+1 dimensions, for which the light cone coordinates $x_R$, $x_L$ transform under worldline diffeomorphisms as scalar densities of appropriate weight.